1. Procedural vs Functional Style
procedural = imperative
cs3180(Prasad)
L13FP

2. Abstracting Expressions
Scale a 2D-point p by a factor c
(define scale
(lambda (c p)
(list
(* c (first p))
(* c (second p)) ) ))
Can abbreviate a fixed and finite number of function applications for readability, modifiability, and reusability.
(* 2 x ) (+ x x) (ROL x) = DOUBLE
cs3180(Prasad)
L13FP

3. Procedural/Imperative vs Functional
Program: a sequence of instructions for a von Neumann m/c.
Computation by instruction execution.
Repetition: Iteration.
Modifiable or updateable variables.
Program: a collection of function definitions (m/c independent).
Computation by term rewriting.
Repetition: Recursion.
“Assign-only-once” variables.
cs3180(Prasad)
L13FP

4. Functional Style : Illustration
Definition : Equations
sum(0) = 0
sum(n) = n + sum(n-1)
Computation : Substitution and Replacement
sum(2)
= sum (2-1)
= …
= 3
cs3180(Prasad)
L13FP

5. Paradigm vs Language Procedural Style Functional Style
i := 0; sum := 0;
while (i < n) do
begin
i := i + 1;
sum := sum + i
end;
Storage efficient
Functional Style
func sum(i:int) : int;
begin
if i = 0 then 0
else i + sum(i-1)
end;
No Side-effect
Recursive call requires allocation of fresh storage for formal arguments (and local variables). This is because after the recursion returns we still have use for the old value of n. (cf. tail -recursion)
cs3180(Prasad)
L13FP

6. Role of Variables Imperative (read/write) i 0 1 2 3 ...
sum
Functional (read only)
i sum1
i sum2
i sum3 3 6 2 3
Storage reused vs
memory freshly allocated each time a call is made 1 1
cs3180(Prasad)
L13FP

7. Bridging the Gap
A tail recursive definition can be automatically optimized for space by translating it into an equivalent while-loop.
func sum(i : int, r : int) : int;
begin
if i = 0 then r
else sum(i-1, i+r)
end
So, Scheme does not have loop-constructs.
In a tail call, the result of the recursive call is the same as the result returned for the original call. So there is no processing of the recursive call result, and there is no need to retain the old values of the formals. In other words, formals can be destructively assigned to.
Recursion is strictly more “expressive” than iteration but in cases where recursion can be cast as an iteration for efficiency, Scheme mandates that the interpreters do so.
cs3180(Prasad)
L13FP

8. Iteration vs Recursion
Recursion = Iteration + Stack
Iteration = Tail Recursion
cs3180(Prasad)
L13FP